How can I add a triangular shape with the thickness of my loop cuts?
I would recommend the following for your workflow:

If you are planning on keeping both your angle, and your stiffeners as one mesh object, then delete your two faces that your triangular stiffener plate will be running over top of first.

To do this go into face mode, select your faces (Hold Shift to select more than one), X >> Only Faces.

Next go into Edge mode.

Next, select your two outer edges (Hold Shift to select more than one) and using W >> E(Bridge Edge Loops). 

NOTE: Repeat this for both triangle loops that get created.

Next Select your triangle edge loop using Alt+Right-Click.

Next hit F to fill in the the loop.